Question

Trigonometric Functions

Answer 1

Find the exact value of each of the remaining trigonometric functions of theta.

\[\csc \Theta = -4, \tan \Theta > 0\]

Answer 2

Alright, just a bunch of identity crunching:

\[\sin{\theta} = \frac{1}{\csc{\theta}} = -\frac{1}{4}\]
Cosine and sine have the same sign, since tangent is positive, so:
\[\cos{\theta} = \sqrt{1-\sin^2{\theta}} = -\frac{\sqrt{15}}{4}\]
\[\sec{\theta} = \frac{1}{\cos{\theta}} = -\frac{4}{\sqrt{15}}\]
\[\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{1}{\sqrt{15}}\]
\[\cot{\theta} = \frac{1}{\tan{\theta}} = \sqrt{15}\]